Numeracy
by Yuuki F
Summary: Mathematical platonism gets called into question.


(if I butchered how you think about platonism, I'm sorry, please chalk it up to artistic license)

Among wolf packs who have functioned together for long periods of time, a sort of unconscious comradery forms between them. They begin to realize things as a group, and in particular they notice dangers well before any individual wolf actually has any specific scent or other sense to catch it. It was in this condition, that Yuki, Koizumi, and Kyon found themselves in the club room. And in the middle of playing a game of chess, Koizumi and Nagato's head suddenly snapped to attention, and soon after there appeared before the trio a platter.

They simply sat in frozen silence. It was an ordinary, silver platter, with a semisphere tin covering its inside. Kyon looked to the other two, who simply sat in a silent reverence towards it. And then he shrugged, having become completely normalized by such events, and did the completely obvious action. He opened the platter.

Kyon grimaced upon seeing what was inside, _Darn it. Just once can't we have some crazy, random thing happen like, I don't know, good cuisine suddenly appear in the club room?_

As he continued to gaze at it. It was as if his vision was at the very edge of being able to process how it looked like. It, at once, appeared as a bowl of three oranges, a tub filled with three bowls, three boats in an ocean, and so on. The three of them continued to stare at it, unable to fully process its appearance. But, for sure, all of them were afraid to touch it. Because of its visual confusion, it was as if it was unstable. However, Yuki outstretched her hand over it.

The other three watched her slowly caress the air on top of it, as if she were trying to sooth it. She then brought her hand back.

"It's the number three."

Kyon blinked, "What?"

Koizumi nodded, "I see."

Kyon looked to Koizumi, "What? What does she mean?"

"Well," Koizumi motioned to the ephemeral mass on the club table, "It is as Miss Nagato said, that is the number three. It is Three."

Kyon shook his head, "W..what?! What the hell does that mean?!"

Koizumi held up his index finger, "One."

He pointed up his middle finger along with his index, "Two."

And then he pointed his ring finger along with the other two, "Three."

When he did this, Kyon noticed-for a short, instantaneous moment-the mass flash, coincident with Koizumi's counting. It seemed as if all of them had noticed, as they were now staring at the mass.

"Interesting," Koizumi muttered.

Kyon shook his head, "Uhm...I'm not sure I still understand."

Koizumi unfolded the palm of his hand towards Kyon, "Have you heard of mathematical platonism?"

Kyon mouthed, "Nope."

Koizumi nodded, "When I refer to objects in speech, I typically refer to something that actually exists in our conventional physical reality. For example," he picked up a chess piece, "This King is white refers to the King piece that I hold in my hand."

He put the chess piece back down, "However, this is one way of viewing the property of the piece, the 'whiteness' is to bound it up with the chess piece. The theory of platonism is a different view holds that that property exists in a higher realm as an Ideal Form and that when we refer to this property, what we are actually doing is referring to this 'whiteness' that **actually exists**."

Kyon shook his head, "But...that's crazy."

Koizumi didn't respond, he merely motioned to the pulsating mass that evidently **was** the ideal form of the number three.

All three stared at Three in wonder, while the notion that their senses could not fully grasp its true form tickled in the back of their minds. And Kyon, for some reason, he felt himself hypnotized by it, and he wanted...well, an absent-minded wonder and curiosity got the better of him. Like a child, he reached out to touch it.

Yuki and Koizumi replied simultaneously, "Don't!"

Kyon snapped back, "Why not?"

"We don't know what it is-"

"There is insufficient data regarding the object, it is too dangerous to proceed directly."

Kyon furrowed his brow, he knew danger when he felt it. This wasn't it. He touched Three.

And, much like his eyesight, his sense differed far too quickly and confusingly for him to realize what was occurring. But...it was like touching all triples of objects in a way. Kyon retracted his arm to the edge of the table again.

Upon noticing that nothing severe happened, Koizumi asked, "So, how was it?"

Kyon shrugged, "Three-ish."

Kyon shook his head again, "But what I don't understand is that...if that is Three, then..."

He pointed to his hands, "How can I have any collection of, say, three fingers, or three hair strands or any of that when Three is," he pointed to the mass, "There."

Koizumi shrugged, "This is just a representation in our realm of it. It must exist in a realm where such nonstandard superposition is entirely plausible."

Kyon blinked, "I understood half of that sentence. Let me try again, isn't even the apparition of such a form inconsistent? Doesn't this mean that anything we say about the number three is verifiable by looking at Three?"

Koizumi nodded, "Yes, which means all truths involving three and discoverable."

"But then if I invent something involving the use of Three...it wouldn't be an invention then?"

Koizumi shrugged, "I guess the existence of Three is evidence of an unalterable, fated, and ultimately non-emergent existence."

Yuki noted, "That is unlikely."

Kyon turned his head to the one who remained silent a suspicious majority of the time in this endeavor, "What? What's wrong with that?"

Yuki replied, "We have to leave."

"Huh? What's wrong."

"The appearance of Three in this simplified reality is causing the elimination of complexity."

Koizumi nodded, "I see, you must think that in order for it to remain consistent, it is a mere temporary construction from the consciousness of Haruhi."

Yuki nodded.

Kyon shook his head, "No, I have a strange feeling it's going to be alright."

Koizumi raised a brow, "If anything challenged the chaos of Haruhi's world, then it would vanish out of existence. I suppose we shall se-"

And just by saying that, the number three vanished.

The three blinked.

Kyon looked to Nagato, "Is it gone?"

She nodded.

Koizumi remained frozen, "It has returned to its plane, I see."

Yuki shook her head, "It never existed in the first place."

They looked to her.

"The entity required a reduction in simplicity for it to exist, this is a property independent of the character, identity, or space of its existence."

Koizumi pointed to Yuki, "Are you saying that...platonism leads to some sort of objective inconsistency with the basis of reality?"

Yuki nodded.

"Then...how did it appear in the first place?"

Yuki shook her head, "It did not."

Kyon hit his palm against the table, "What are you talking about, it was right here!"

"The data in this space was manipulated to have a simulated psuedo-cognition of that event, but there is not evidence that points to that event having happened."

Koizumi stroked his chin, "You're saying that our memories of it having existed were planted?"

Yuki nodded, "That is a possibility."

Koizumi shook his head, "It is also just as likely that that is how we processed the events in order for the current realm to remain self-consistent."

Yuki and Koizumi stared intently at each other, and Kyon noticed that...this was one of the rare times that Koizumi publicly disagreed with an action of Yuki's, instead of telling him slyly and behind the others' backs. In fact, the occurrence was coupled with another rare event: Koizumi looked mad. The kind of rage that one feels upon taking an insult far too personally. A kind of rage of...someone attacking his ideology.

Kyon thought, _Moreover, each position was entirely consistent with their experiences. Koizumi regularly had experience with an inner realm that contained manifestations of Haruhi's anger. So, another realm containing or __**being**__ the manifestation of things like the number three is a perfectly plausible thing. On the other hand, the possibility of the existence of mere concepts like three implied that the vast swaths of universal truth were not emergent or invented, but rather discovered. Since, if an entity such as the number three actually did exist, then perceiving truths regarding it would be immediately comprehensible from simply observing, rather than pontificating about it. And if Miss Nagato really did believe that Haruhi was some form of auto-evolving superbeing, then the physical manifestation and existence of a concept such as three would be a blow to such a-_

Kyon shook his head, he couldn't even understand what he was saying in his head. He decided to take it with a grain of salt.

Koizumi continued his questioning, "If this was just some minor mass hallucination, do you have any idea what caused it?"

Kyon just had to laugh at the silliness of the entire affair, he shrugged, taking a seat, "Whatever it was, it was probably sponsored by the number three."


End file.
